For what value of $k$ does the equation $x^2+10x+y^2+6y-k=0$ represent a circle of radius 6?
Solution: Completing the square, we can rewrite this equation as $(x+5)^2-25+(y+3)^2-9=k$, or $(x+5)^2+(y+3)^2=34+k$. Because this equation must represent a circle of radius 6, we need $34+k=6^2=36$, so $k=\boxed{2}$.